Mathematical Modeling · 8.1.1
What is mathematical modelling?
Students describe what mathematical modelling is and the cycle it follows: taking a real-life problem, making simplifying assumptions, representing the situation with an equation, function or graph, solving it, then interpreting and verifying the result against the original situation, revising the model if it does not fit, since modelling repeats rather than stopping after one pass.
The official learning standard (8.1.1)
“Explain Mathematical Modeling.”
What it means
Students describe what mathematical modelling is and the cycle it follows: taking a real-life problem, making simplifying assumptions, representing the situation with an equation, function or graph, solving it, then interpreting and verifying the result against the original situation, revising the model if it does not fit, since modelling repeats rather than stopping after one pass.
How it is examined
Mostly tested through short explanation or labelling questions: Paper 1 may ask students to name or order the phases of the modelling cycle, or identify which phase a given action (such as stating an assumption) belongs to. Paper 2 usually embeds this understanding inside a full modelling problem rather than asking for a bare definition.
Worked example
A town's water supplier notices that daily water usage seems to rise by roughly the same amount each year. Explain, step by step, how mathematical modelling would be used to study this situation, from identifying the problem to checking the final result.
- Phase 1, Identify the real-life problem: recognise that daily water usage rises year by year, and decide what needs to be found, such as a way to predict future usage.
- Phase 2, Make assumptions: simplify the situation, for example assuming usage increases by roughly the same amount each year (a constant rate), and ignoring unusual events such as droughts.
- Phase 3, Represent and solve: choose a suitable mathematical form, such as a linear function U = a + bt where U is usage and t is time in years, use given data to find a and b, then solve for the required year.
- Phase 4, Interpret and verify: check whether the model's prediction is realistic and matches other known data; if it does not fit well, revise the assumptions (for example, allow the rate to change) and repeat the cycle.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How many phases does the mathematical modelling cycle have?
Four: identifying the real-life problem, making simplifying assumptions, representing the situation mathematically and solving it, and interpreting and verifying the result. If the result does not fit the real situation well, the cycle repeats from the assumptions stage with a revised model.
Why do we need to make assumptions at all?
Real situations are usually too complicated to describe exactly, so assumptions simplify them into something that can be represented by an equation, function or graph, for example, assuming a constant rate of change. Without assumptions, forming a workable mathematical model would often be impossible.
What does 'verifying' the model actually mean?
Verifying means checking the model's result against real data or common sense, for example, comparing a predicted value with an actual measured value, or checking that the answer has a realistic size and sign. If the model's prediction does not match reasonably well, the assumptions or the model itself need to be revised.